Assignment 6:

Problem: Given three points A, B, and C.  Draw a line intersecting AC in the point X and BC in he point Y such that AX=XY=YB.

The following are steps that I followed in order to solve this problem:

1. Construct an angle ACB like the one given.  Click here to view this angle.

2. Construct a segment connecting point A and point B.  Click here to view this segment.

3. Construct a random point on segment AC, point P.   Click here to view this point.

4. Construct a line parallel to CB through point P.  Click here to view this line.

5. Construct a circle with the center at P passing through point A.  Click here to view this circle.

6. Construct the intersection point between the constructed circle from Step 5 and the constructed parallel line from Step 4.  Name this intersection point D.  Click here to view this intersection point.

7. Construct a circle with the radius of segment DP and center at point D.  Click here to view this circle.

8. Construct the intersection point between the circle constructed in Step 7 and the segment AB.  Name this intersection point E.  Click here to view this intersection point.

9. Construct the segment DE.  Click here to view this segment (shown in red).

10. Construct a parallel line between the segment DE and the point P.  Click here to view this line.

11. Construct the intersection point between the parallel line constructed in Step 10 and the circle constructed in Step 5 (center at P).  Name this intersection point F.  Click here to view this intersection point.

12. Construct segment PD and segment FE.  Click here to view the two constructed segments.

13. Construct segment AF.  Click here to view this segment (shown in green).

14. By selecting point A and segment AF, extend segment AF by constructing a parallel line.  Click here to view the parallel line.

15. Construct the intersection point between segment BC and the parallel line constructed in Step 14.  Name this intersection point Y.  Click here to view this intersection point.

16. Construct a circle using segment YB as the radius and point A as the center.  Click here to view this circle.

17. Construct the intersection point between the circle constructed in Step 16 and the segment AC.  Name this intersection point X.  Click here to view this intersection point.

18. Construct the segment XY.  Click here to view this segment (shown in pink).

19. Measure the lengths of the segments XA, YB, and XY to make sure that they are all equal.  Click here to view the measurements.

20. IT WORKS!!!!